Parabola Flashcards
What is the standard equation of the parabola ?
y^=4ax
What is latus rectum of a parabola ?
Latus rectum of a parabola is a special type of double ordinate which passes through the foci. Focus of parabola is midpoint of latus rectum
On parabola , what is the perpendicular distance of focus to directrix equal to ?
Half the directrix.
In parabola , what is the vertex of parabola ?
Vertex of parabola is the middle point of the focus and point of intersection of directrix and axis.
When are two parabolas considered equal ?
Two parabolas are considered equal when they have the same latus rectum.
What is the coordinate of the foci of curve y^=4ax ?
(a,0)
What is the equation of directrix of curve y^=4ax
x=-a
What is the equation of axis of the curve y^= 4ax
y=0
What are the parametric coordinate of parabola of equation y^=4ax
Any point on parabola y^=4ax is (at^, 2at), it is referred as point t. T is parameter , it varies from point to point.
What is the minimum length of focal chord ?
Minimum length of focal chord is 4a ie length of latus rectum.
What is focal distance of a point on the parabola ?
Focal distance is the distance between point P on parabola and focus S, ie PS. It’s equal to a+x
What is the tangent at a point (x1,y1) lying on the parabola ?
yy1= 2a(x+x1)
What is the slope form of tangent to parabola ?
y= mx + a/m
Point or contact is [(a/m^),(2a/m)]
What is the director circle of parabola ?
Director circle of parabola is x + a= 0 ie parabolas own directrix.
What is the normal at point (x1,y1) on the parabola ?
Slope of normal is -y1/2a.
Also it passes through (x1,y1)
It’s eq y-y1=-y1/2a(x-x1)
What is the normal of parabola in slope form ?
If m is the slope of normal , then it’s equation is y=mx - 2am -am^3. It will cut the parabola at point (am^,-2am)
What can you say about semi latus rectum of the parabola y^=4ax?
Semi latus rectum is the harmonic mean between the segments of any focal chord of the parabola.
What is the coordinates of the orthocentre of the triangle formed by three tangents of the parabola y^=4x?
It lies on the directrix and had coordinates
-a,a(t1+t2+t1t2t3)
What is the shortest normal chord of any parabola with latus rectum =4a?
6a√3
